Scaling of quasi-brittle fracture: Boundary and size effect

A boundary effect model recently developed for scaling of quasi-brittle fracture is used to study the common size effect on strength and fracture toughness of finite-sized specimens. An equivalent crack length is adopted following the boundary effect model and used to measure the distance of a crack tip to the front and back specimen boundaries. This equivalent crack leads to a simplified asymptotic solution for finite-sized specimens akin to that for a large plate with a small edge crack. The two common failure criteria, the strength and the linear elastic fracture mechanics (LEFM) KIC criteria, are taken as two asymptotic limits. The transition from the strength to toughness criterion is then given by the asymptotic solution. The recent asymptotic model for finite-sized specimens/structures is applied to geometrically similar specimens of a fixed α-ratio, and specimens of identical size, but different α-ratios.